MathDB
Geometric probability

Source:

December 18, 2005
probabilitynumber theoryrelatively prime

Problem Statement

Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. The probability that some three of the segments form a triangle whose vertices are among the ten given points is m/n,m/n, where mm and nn are relatively prime positive integers. Find m+n.m+n.